Heterogeneous Morphology and Dynamics of Polyelectrolyte Brush Condensates in Trivalent Counterion Solution

Abstract

Recent experiments have shown that trivalent ion, spermidine 3+ , can provoke lateral microphase segregation in DNA brushes. Using molecular simulations and simple theoretical arguments, we explore the effects of trivalent counterions on polyelectrolyte brushes. At a proper range of grafting density, polymer size, and ion concentration, the brush polymers collapse heterogeneously into octopus-like surface micelles. Remarkably, the heterogeneity in brush morphology is maximized and the relaxation dynamics of chain and condensed ion are the slowest at the 1:3 stoichiometric concentration of trivalent ions to polyelectrolyte charge. A further increase of trivalent ion concentration conducive to a charge inversion elicits modest reswelling and homogenizes the morphology of brush condensate. Our study provides a new insight into the origin of the diversity in DNA organization in cell nuclei as well as the ion-dependent morphological variation in polyelectrolyte brush layer of biological membranes.Polyelectrolyte brushes are ubiquitous in biological systems. As the main component of outer membrane in Gram-negative bacteria, lipopolysaccharides, consisting of charged O-polysaccharides side chains, form a brush layer and mediate the interaction of bacteria with their environment [1]. For vertebrates, negatively charged polysaccharide hyaluronic acids play a vital role in the organization of pericellular matrix [2,3]. Double-stranded DNA brushes on a biochip [4] at a cell-like density (∼ 10 4 kb/µm 3 ) have been developed as a platform to study cell-free gene expression [5]. Due to the negative charges along the backbone, this synthetic system behaves like a well-defined strong polyelectrolyte brush [5], the height of which can be varied by modulating the ionic strength of monovalent salt (NaCl) solution and the grafting density [6]. Recently, it has been reported that trivalent counterions, spermidine 3+ (Spd 3+ ), can induce a collapse transition of DNA brush into fractal-like dendritic macroscopic domains [7]. The heterogeneous morphology of DNA condensate points to polyamine-mediated regulation of local DNA configuration and gene expression [8,9], underscoring the importance of understanding the effects of multivalent counterions on polyelectrolyte brush [10,11]. Compared with uncharged polymer brushes in good or poor solvent, the electrostatic interaction and osmotic pressure, which are readily controlled by the salt concentration and pH, yield additional flexibilities in manipulating polyelectrolyte brushes, and thus holding promise for its wide applications [12,13].Conventional theoretical approaches, successful in explaining the behaviors of polyelectrolytes in monovalent salt solutions [11,14,15], are of limited use, particularly, when multivalent counterions are at work. For example, the solution to the mean-field PoissonBoltzmann theory [16] fails to account for phenomena such as ion condensation, charge over-compensation, and collapse of like-charged polymers [17][18][19][20]. A prediction from a nonlocal den...

From octopus to dendrite—Semiflexible polyelectrolyte brush condensates in trivalent counterion solution

“…Depending on the chain stiffness, brush condensates adopt diverse morphological patterns that vary from semi-spherical octopus-like micelle domains to cylindrical bundles of rigid chains which protrude from the grafting surface. It was shown that when the grafting density is in a proper range, multivalent counterions can collapse flexible PE brush even in good solvent into octopus-like surface micelles displaying substantial lateral heterogeneity [42][43][44] , which has recently been confirmed experimentally for polystyrene sulfonate brush condensates in Y(NO 3 ) 3 solution 45 .…”

Structure and Functionality of Polyelectrolyte Brushes: A Surface Force Perspective

“…Liu et al. showed that the brush chains collapsed heterogeneously into “octopus‐like” surface micelles within a certain range of grafting density, polymer size, and ion concentration . Jackson et al.…”

“…[34] Liu et al showed that the brush chains collapsed heterogeneously into "octopus-like"s urface micelles within ac ertain range of grafting density,p olymer size, and ion concentration. [35] Jackson et al demonstrated that, whilst ostensibly forming similarm icellar structures,s olvophobic collapsed brushes and multivalent-ion-collapsed brushes exhibited distinct mechanistic and structural features. [36] By using a combination of AFM, SFA, and MD simulations, Yu et al confirmed that solvophobic and multivalent-ion-inducede ffects work in concert to drivet he strong phase separation of polyelectrolyte brushes, with electrostatic bridging of polyelectrolyte chains playing an essential role in the formation of the lateral structurali nhomogeneities ( Figure 3b).…”

Architecture of human interphase chromosome determines the spatiotemporal dynamics of chromatin loci

“…The scale-dependent relaxation dynamics of the chromatin domain is quantified using the time evolution of intermediate scattering function F k (t) (43,44) calculated at different length scale (∼ 2π/k) ( Fig. 5B).…”

“…The scale-dependent relaxation dynamics of the chromatin domain is quantified using the time evolution of intermediate scattering function F k (t)(44,45) calculated at different length Effects of active force on chromosome organization and dynamics. (A) MSD of active and inactive loci compared with those under passive condition.…”